56). Consider the following statements
Area of segment of a circle is less than area of its corresponding sector.
Distance travelled by a circular Wheel of diameter 2d cm in one revolution is greater than 6d cm.
Which of the above statements is/are correct?

A). Only I

B). Only II

C). Both I and II

D). Neither I nor II

View Answer

Correct Answer: Both I and II

We know that, area of segment (PRQP) = Area of sector (OPRQO)- Area of \( \Large \triangle OPQ\)

=\( \Large \frac{\pi r^{2}\theta}{360}-\frac{1}{2}r^{2}sin\theta \)

so, the area of a segment of a circle is always less than area of its corresponding sector.

II. Distance travelled by a circular wheel of diameter 2d cm in one revolution

= \( \Large 2\times 3.14\times d \)=6.28d

which is greater than 6d cm.

57). The radius of a circle is so increased that its circumference increased by 5%. The area of the circle, then increases by

A). 12.5%

B). 10.25%

C). 10.5%

D). 11.25%

View Answer

Correct Answer: 10.25%

Increase in Circumference of circle = 5% Increase in radius is also 5% Now, increase in area of circle =\( \Large \left(2a+\frac{a^{2}}{100} \right)% \)

where,a=increase in radius

=\( \Large \left(2\times 5+\frac{5\times 5}{100} \right)\% \)=10.25%

58). The area of a circle is increased by 22 sq cm when its radius is increased by 1 cm. Find the original radius of the Circle.

A). 6 cm

B). 3.2 cm

C). 3 cm

D). 3.5 cm

View Answer

Correct Answer: 3 cm

Let original radius be r.

Then, according to the question,

\( \Large \pi (r+1)^{2}-\pi r^{2} \)=22

=> \( \Large \pi\times [(r+1)^{2}-r^{2}] \)=22

=> \( \Large \frac{22}{7}\times (r+1+r)(r+1-r) \)=22

=> 2r+1=7 => 2r=6

r=\( \Large \frac{6}{2} \)=3 cm

59). What is the area of the larger segment circle formed by a chord of, length 5 cm subtending an angle of 90 degree at the centre?

60). A person observed that he required 30 s time to cross a circular ground along its diameter than to cover it once along the boundary. If his speed was 30m/min, then the radius of the circular ground is \( \Large (take \ \pi = 22/7) \)